The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
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Difference between space of reference and system of coordinates

In the book "The meaning of the relativity" by A. Einstein, it is referring to two different concepts: space of reference and system of coordinates. What it is the difference? It says: "we ...
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What is meant by rest in rest-mass?

As far as I know only photons are considered to have no rest-mass. In common words when it doesn't move it 'disappears'. Electrons and quarks should have a rest-mass. But are they really at rest? ...
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The criteria of light

My question is regarding if the "speed of light" 299,792,458 m/s should only apply to certain frequencies of light/colors/amplitude and most the medium in which it travels at 299,792,458 m/s . Shouldn'...
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Time dilation: time shortest where events occur at same place?

In his book Simply Einstein Richard Wolfson describes time dilation this way: "The time between two events is shortest when measured in a reference frame where the two events occur at the same place." ...
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Observer travelling near speed of light observing a laser pointer seeing photons at speed of light?

I'm a little confused by the following classic example about the speed of light being constant for all observers (paraphrasing): Jack and Jill are both travelling at a significant portion of the ...
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How do I draw the Minkowski diagram of a event in two inertial systems when t=t'=0?

An Introduction to Mechanics" by David Kleppner & Robert Kolenkow, 1st Edition, 12.1 Assume that v= 0.6c . Find the coordinates in S' of the following events: a). x=4 [m], t= 0[s] b). x=4 [m], ...
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What is relationship between electromagnetic mass and rest mass?

Is there a direct equation which compares rest mass $m_°$ and electromagnetic mass $m_{em}$? Nothing on web I found. $m_{em} = \frac{4 E_{em}}{3c^2}$ 4/3 problem The final solution of the ...
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Composition of Lorentz Transformations

If a particle is moving in the $x$-direction with velocity $c/2$, then the Lorentz transformation $\Lambda = \begin{pmatrix}\gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma &...
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Relevance of spinor in relativistic (classical) electrodynamics

I'm following a course about relativity and electrodynamics (not the "quantum" one), and the lecture notes introduces the concept of spinor by a map between an orthogonal basis in Minkowski spacetime ...
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110 views

Is the speed of light constant in all directions?

Consider the shape of the waveform emitted by a moving source: (with the horizontal axis "x" and the vertical axis "y"). According to the stationary observer, the wavefront of a short pulse ...
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Presentism: doesn't everything exist at the same moment? [closed]

The Help Center recommends I 'fix' this question: (original question) "It seems self-evident that everything exist in the Now. Notwithstanding time-dilation and different rates of the passage of ...
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Do we know why there is a speed limit in our universe?

This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to $c$...
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Special Relativity: Verifying a general boost matrix is in the Lorentz group

I'm attempting the problem shown below. Using the hint, I have so far found: \begin{align}B^T \eta B &= \begin{pmatrix}\gamma & -\gamma\beta^j \\ -\gamma \beta_k & \delta_k^j+\frac{(\...
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If photons can exert a change in momentum when being reflected, what leads us to conclude they have zero mass? [duplicate]

It is well known that gravity affects light. It is also known that light can impart a change in momentum to objects when being reflected. This leads me to think that photons have momentum and ...
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343 views

Time-reversed twin paradox

This started with wondering about the nature of certain physical quantities under time-reversal - chiefly, that acceleration retains its magnitude and direction at a given time regardless of the '...
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Action of a massive free point-particle in relativistic mechanics

I was reading about the formulation of mechanics in special relativity and found that the action for a massive free point-particle as $$ S = -mc\int_a^b ds $$ So, I did a few observations, ie. $$ S =...
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Are gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
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Is Young's Modulus a Lorentz Scalar?

If a spring is at rest and lies along $X$ axis in a frame $O$ with a spring constant $k_{0}$ then its spring constant in a frame $O'$ which is moving with a speed $v$ at an angle $\theta$ with the $X$ ...
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258 views

Is it possible to determine maximum frequency of a disc using a relative circumference?

On Wikipedia there is an article that shows how to calculate the relativistic effects on a rigid spinning disc, I am referencing the formula under the "Ehrenfest's argument" section in the link. The ...
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Speed of Dark experiment, does it *really* travel faster than light? [duplicate]

I have seen many folks doing this Moon shadow experiment concluding that shadow from point A on the Moon can travel to point B on the Moon faster than light. What I fail to understand here (and I am ...
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92 views

Can't reach speed of light, but relative to who?

Imagine a stationary person (with respect to a spaceship) floating in space and looks at a clock on the spaceship going 0.5c and sees it's clock ticking slower than his own, and concludes that it is ...
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Were the Michelson-Morley results a surprise?

How unexpected were the Michelson-Morley experiment results? Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?
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Spacetime and quantum mechanics

In special relativity, the particle has a fixed world line in spacetime. So its whole trajectory is determined. But how can we represent the world line of the particle in spacetime when we take ...
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A photon lives life as a flat-lander? [duplicate]

Think length contraction... I was thinking about going close to the speed of light the other day, and I was thinking about the idea that, if you went close to the speed of light, time would slow down ...
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Why are usually 4x4 gamma matrices used? [duplicate]

As far as I understand gamma matrices are a representation of the Dirac algebra and there is a representation of the Lorentz group that can be expressed as $$S^{\mu \nu} = \frac{1}{4} \left[ \gamma^\...
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Why shift in fringe is expected in Michelson Morley Experiment?

When I (beginner) learnt Michelson Morley experiment, it was expected that there should be a shift in the fringe pattern when the setup was rotated by 90 deg if the presence of ether is true. But why ...
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Is an extended spring gain mass from potential energy? [duplicate]

Is it true that when a spring is extended, potential energy is stored in spring and result in gain of mass of the spring?
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SR and a rotating observer [closed]

What if an observer took a particle placed it some distance away from himself and began to circle the particle approaching the speed of light. Would the observer himself observe that the circle is ...
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99 views

Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments? If the law of conservation of linear momentum ...
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A question from “The meaning of the relativity, by A.Einstein” - Lorentz transformations [duplicate]

Let $K$ and $\bar K$ be two cartesian co-orditate systems in $\mathbb{R}^3$. The element: $$s^2=(\Delta x^1)^2+(\Delta x^2)^2+(\Delta x^3)^2$$ is an invariant in all co-ordinate system. I want prove ...
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How does the speed of light affect energy? [duplicate]

According to Einstein's theorem E=mc2, energy equals to product of mass and speed of light. How does the speed of light affect energy? If it is so, then why is the specific value for the speed of ...
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Electric field around a moving charge

A moving charge has magnetic field around it. Is it just increased electric field in relativistic frame? If yes, does a moving charge has more electric field around it?
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Lorentz transformation and symmetries of the Lagrangian [duplicate]

Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations ...
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Relativistic Rocket Fuel Requirements

I am trying to reconcile two different calculations of fuel for a 1g constant acceleration/deceleration trip to Alpha Centauri. One found here (http://math.ucr.edu/home/baez/physics/Relativity/SR/...
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86 views

Wave operator applied to electromagnetic field tensor

I'm trying to understand an argument in "An introduction to general relativity" by Hughston and Todd (p37). Let $F_{ab}$ be the electromagnetic field tensor, I'm trying to show: $$\Box F_{ab} = -4 \...
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Relativity paradox with mirrors and light pulses

Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram). From the point of view of the lab frame, the apparatus is all moving to the left at ...
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Is there any way to justify or derive the form of the Lorentz force from relativity theory?

Lorentz force is in this form: $$\vec{F}=q[\vec{E}+\vec{u}\times\vec{B}]$$ As we know, it is Lorentz-invariant. Is there any way to justify or derive its form from relativity theory?
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Poincare Group (Wald, Chapter 4 Page 59)

In Wald's text on general relativity, he mentions that in special relativity, many different global inertial coordinate systems are possible and can be put into one-to-one correspondence with elements ...
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What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
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Relativistic mass of electron in a potential [closed]

An electron is accelerated through a 6 MV potential difference. what is the mass of the electron at the end of the path?
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254 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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Variation of spin in the rest frame of an electron in an external magnetic field

In Jackson's Classical Electrodynamics, the equation of motion for the angular momentum $\textbf{s}$ of an electron in an external magnetic field is given by (eq. 11.101) $$\left(\frac{d\textbf{s}}{dt}...
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1answer
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Why would two inertial frames be distinguishable, if the coordinate of an event perpendicular to the motion would be different? [closed]

This question arises from the classical example: imagine a laboratory frame, and a space shuttle frame, the space shuttle moving in the laboratory frame with a constant velocity, let's say in the $x$ ...
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2answers
174 views

Is the $i$ in QM a time component in disguise?

In SR, it is possible to replace the Minkowski metric $\eta_{\mu\nu}$ with a (pseudo) euclidean metric $\delta_{\mu\nu}$ provided that time is measured in imaginary units. I was wondering if the same ...
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2answers
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Do any two points in Minkowski spacetime determine a unique line?

Any two points in a Euclidean space determine a unique line, but I wasn't sure if this result generalized to Minkowski spacetime given that the latter is not a Euclidean 4-space, but is, instead, a ...
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1answer
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Will the speed of gravity and the speed of light always be the same?

I have been considering the following though experiment: If the entire sun were to disappear at once, would we feel it first due to the sudden drop in gravity or see it first? The answer I have come ...
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Does Heat Cause Time Dilation?

Since heat is defined as the movement of molecules, and because of relativity time slows for faster moving objects, would a hot object be in a slower time frame then a cooler object, because the hot ...
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Proper time for an accelerating object

As far as I have read so far, proper time is the time measured on the clock of an inertial frame moving uniformly with respect to another inertial frame. The concept and the mathematical expression ...